Perturbation analysis of the extinction probability of a Markovian binary tree
| Autor: | Pei-Chang Guo, Yunfeng Cai, Jiang Qian, Shu-Fang Xu |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Numerical Analysis
Algebra and Number Theory Binary tree Extinction probability Markov process Perturbation (astronomy) System of linear equations Residual symbols.namesake Quadratic equation symbols Discrete Mathematics and Combinatorics A priori and a posteriori Applied mathematics Geometry and Topology Mathematics |
| Zdroj: | Linear Algebra and its Applications. 475:11-27 |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2015.02.006 |
| Popis: | The extinction probability of the Markovian Binary Tree (MBT) is the minimal nonnegative solution of a Quadratic Vector Equation (QVE). In this paper, we present a perturbation analysis for the extinction probability of a supercritical MBT. We derive a perturbation bound for the minimal nonnegative solution of the QVE, which is a bound on the difference between the solutions of two nearby equations in terms of the perturbation magnitude. A posteriori error bound is also given, which is a bound on the distance between an approximate solution and the real solution, in terms of the residual of the approximate solution. Numerical experiments show that these bounds are fairly sharp. |
| Databáze: | OpenAIRE |
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